How are easing functions created for animation?

Question

css

I'm into web animation and I love sawing bikes. More recently, I learned how to use formulas for easing functions for animation on requestAnimationFrame. And now I'm tormented by the question - how exactly do people create these formulas?
If suddenly someone does not understand what this is about, here are two sites dedicated to easing:
1) timotheegroleau.com/Flash/experiments/easing_funct... (there is even a constructor on this one)
2) gizma.com/easing
Specifically, up to some I can think of a simple quadratic function myself and even came up with all sorts of other garbage, playing with numbers, but I don’t understand how people create all sorts of elastic functions. Is it really just that someone has been playing with numbers for a long time and hard to get, for example, this formula:

function outElasticBig(t, b, c, d) {
  var ts = (t/=d)*t;
  var tc = ts*t;
  return b+c*(56*tc*ts + -175*ts*ts + 200*tc + -100*ts + 20*t);
}

I don’t believe in such miracles, everything here is definitely tied to mathematics, and I either didn’t study this at the university, or I have already forgotten everything :(

Answer 1

This is called "interpolation theory". You can start with the Lagrange polynomial . Studied in the courses "Mathematical Modeling" and "Numerical Methods".